It depends.
The classic Oreo cookie is made using the same main ingredients, With some substitutions like in Canada, where the vegetable oil is coconut oil. None of these ingredients are currently of animal origin:
- Sugar
- Unbleached enriched flour (wheat flour, niacin, iron, thiamine mono-nitrate (vitamin B1), riboflavin (vitamin B2), folic acid)
- High oleic canola oil and/or palm oil and/or canola oil
- Cocoa (treated with alkali)
- High-fructose corn syrup
- Leavening agent (baking soda and/or monocalcium phosphate)
- Corn starch
- Salt
- Soy lecithin
- Vanillin
- Chocolate
- Palm oil
The contradictions seem to stem from the fact that the manufacturers themselves state that they are not vegan. According to the official UK site FAQ (emphasis mine):
No, Oreo have milk as cross contact and therefore they are not suitable for vegans.
However, some vegans including myself, and although I would rather buy products from brands that are entirely cruelty-free, would not deem them non-vegan solely because of cross-contamination risk.
This was different in the past as milk whey was used as an ingredient for the filling in the EU market.
The bottom line is:
Ingredients of this heavily processed, industrialized snacks change often as they are always trying to reduce costs. Try to stay away from this gamble and if there isn't a choice, carefully read the ingredients on that particular package. Of course, also decide for yourself whether "might contain traces of milk" is acceptable.